Many people consider this to be the first book in a GREAT mystery series. Even those that have read other books in the series first always wonder how Lynley and Havers actually meet each other and start solving mysteries. In short, A Great Deliverance is the book that answers that question.
The English detectives here are Detective Sergeant Barbara Havers and Inspector Thomas Lynley. The first mystery the readers come upon is a local farmer who is decapitated while on the job. Father Hart is on his way to Scotland Yard in order to stop some arguing among the investigators. Roberta (the daughter) is found next to her dad's body and confesses to the murder easily. Father Hart disagrees. When Scotland Yard becomes involved, both Havers and Lynley are called upon.
It is at this point in the novel when we are given some background on the detectives. Lynley is an "earl," actually, and a member of the "old rich" who has no need of employment. Lynley simply feels obligated to do what comes naturally to him: solve mysteries. Havers has just as many issues, just different ones. She is biased, prejudiced, impulsive, and all over the place in regards to emotion. What she lacks in intuition, she makes up with hard work. They are a good team, but it doesn't quite seem that way until later in the series.
In conclusion, you have to understand this book is more about character development of Havers and Lynley than with a stupendous mystery plot. Yes, Lynley and Havers solve the mystery by proving that the large girl wielding the axe couldn't have possibly lopped off her father's head. In the process, we get to laugh at the mismatched (and yet BRILLIANT) puzzle-solving pair of Lynley and Havers.